Question Number 200759 by brahim_mekkaoui last updated on 23/Nov/23 $$\mathrm{let}\:\mathrm{u}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{n}}{\mathrm{k}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} }\:\mathrm{for}\:\mathrm{n}\in\mathbb{N}_{>\mathrm{0}} \:\: \\ $$$$\mathrm{show}\:\mathrm{that}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}_{>\mathrm{0}} } \mathrm{is}\:\mathrm{increasing}. \\ $$ Terms of…
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Question Number 200741 by Rydel last updated on 22/Nov/23 $$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{{a}\mathrm{sin}\:{x}−{x}\mathrm{sin}\:{a}}{{x}−{a}} \\ $$ Commented by JDamian last updated on 22/Nov/23 really? Answered by JDamian last…
Question Number 200632 by pascal889 last updated on 21/Nov/23 $$\boldsymbol{\mathrm{help}}\:\boldsymbol{\mathrm{me}}\:\boldsymbol{\mathrm{derived}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{formular}}\:\boldsymbol{\mathrm{of}} \\ $$$$\:\boldsymbol{\mathrm{motion}} \\ $$ Commented by mr W last updated on 21/Nov/23 $${do}\:{you}\:{really}\:{think}\:{this}\:{is}\: \\ $$$${appropriate}?\:{this}\:{is}\:{like}\:{when}\:{i}\:{ask}…
Question Number 200622 by sonukgindia last updated on 21/Nov/23 Answered by Rasheed.Sindhi last updated on 21/Nov/23 $$\bullet\left({a}+{b}+{c}\right)^{\mathrm{2}} =\mathrm{4}^{\mathrm{2}} =\mathrm{16} \\ $$$$\:\:\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +\mathrm{2}\left({ab}+{bc}+{ca}\right)=\mathrm{16} \\…
Question Number 200617 by sonukgindia last updated on 21/Nov/23 Answered by Frix last updated on 21/Nov/23 $${x}+{a}={y}^{\mathrm{2}} \\ $$$${y}+{a}={x}^{\mathrm{2}} \\ $$$${x}−{y}={y}^{\mathrm{2}} −{x}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} −{y}^{\mathrm{2}}…
Question Number 200619 by sonukgindia last updated on 21/Nov/23 Answered by witcher3 last updated on 21/Nov/23 $$\mathrm{I}_{\mathrm{9}} =\mathrm{2}\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{x}^{\mathrm{a}} }{\mathrm{c}+\mathrm{kx}^{\mathrm{b}} }\mathrm{dx} \\ $$$$\mathrm{in}\:\infty\:\mathrm{c}+\mathrm{kx}^{\mathrm{b}} \sim\mathrm{x}^{\mathrm{b}}…
Question Number 200618 by sonukgindia last updated on 21/Nov/23 Commented by Frix last updated on 21/Nov/23 $$\sqrt{\mathrm{2}}−\mathrm{1} \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 200574 by Harnada last updated on 20/Nov/23 $${sorry}\:{mr}\:{W} \\ $$ Commented by mr W last updated on 20/Nov/23 $${for}\:{what}? \\ $$ Commented by…
Question Number 200575 by sonukgindia last updated on 20/Nov/23 Answered by AST last updated on 20/Nov/23 $$\frac{{ra}}{\mathrm{2}}=\frac{{bx}}{\mathrm{2}}\Rightarrow{ra}={bx};{x}=\sqrt{{r}^{\mathrm{2}} −{a}^{\mathrm{2}} };{b}={r}−{a} \\ $$$${ra}={bx}\Rightarrow{ra}=\left({r}−{a}\right)\left(\sqrt{{r}^{\mathrm{2}} −{a}^{\mathrm{2}} }\right) \\ $$$$\Rightarrow\mathrm{2}{r}={a}\underset{−}…